## The Binary Stress Model for Graph Drawing

- Yehuda Koren, Ali Çivril
- Graph Drawing
- 2008

- 2016

Many problems can be presented in an abstract form through a wide range of binary objects and relations which are defined over problem's domain. In these problems, graphical demonstration of defined binary objects and solutions is the most suitable representation approach. In this regard, graph drawing problem discusses the methods for transforming combinatorial graphs to geometrical drawings in order to visualize them. This paper studies the force-directed algorithms and multi-surface techniques for drawing general undirected graphs. Particularly, this research describes force-directed approach to model the drawing of a general graph as a numerical optimization problem. So, it can use rich knowledge which is presented as an established system by the numerical optimization. Moreover, this research proposes the multi-surface approach as an efficient tool for overcoming local minimums in standard force-directed algorithms. Next, we introduce a new method for multi-surface approach based on fuzzy clustering algorithms. 1. Introduction Graphs are used in many scientific fields like computational biology [1] or software engineering [2]. Although graphs theory and algorithms are one of the oldest and most studied area in field of computer sciences, graph drawing problem is rather new. Despite the novelty of studies in this field, the foundation for appearance of graph drawing as a practical art goes back long before development of computer sciences. In all scientific fields, researchers use graphs to show systems which are formed by a large amount of interactive elements, especially when these single elements are simple. For example, electrical engineers draw graphs to represent circuits and social science experts draw graphs for group interactions. However, the most widely uses for graph drawing is in the field of computer and information technology which contains many areas like software architecture [3] or semantic networks [4]. Graph layouts have a considerable impact on time that user requires for understanding its related data. In addition, a graph with poor layout could be confusing and misleading. The purpose of graph drawing is the recognition of the nodes position and edges routing in a manner that clearly shows the structure of the related data. Generally, there are two types of algorithms for graph drawing. First kind of algorithms focus on special type of graphs like Hamming's graphs and trees. Second type pays attention to general graphs and they are mostly different based on their optimization strategies. This research investigates general graphs and uses a combination of force-directed algorithms and multi-level techniques …